A joint finite-difference and FFT full vectorial beam propagation scheme

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Abstract
A full vectorial beam propagation scheme is developed and it is applied on 3-dimensional waveguide structures. The formulation is based on the coupled wave equations for the transverse electric field. Each propagation step is performed by utilizing both the FFT and a finite-difference implementation. Under this perspective the offered advantages of FFT and finite-differences are exploited within a single propagation step resulting in a joint propagation scheme. The scheme is applied on a step-index circular fiber where analytical solutions are readily available for cross-checking. Moreover, the dependence of the phase constant on the reference refractive index is discussed. The polarized modes and the effective mode indices are derived in the case of rib waveguides by performing propagation along imaginary distance. Further, the rib waveguide coupler is examined and the energy transfer is simulated.